Modeling and tracking phase and frequency offsets in low-precision clocks

This paper considers the problem of tracking carrier phase offsets in distributed multi-input multi-output (DMIMO) systems. Unlike conventional MIMO systems, each antenna in a DMIMO system is driven by an independent oscillator. To achieve coherent communication, e.g., distributed beamforming and/or nullforming, the time-varying offsets of these oscillators must be accurately tracked and compensated. While Kalman filtering has been used to optimally track phase and frequency offsets, it is well-known that the Kalman filter requires exact knowledge of the process and measurement noise parameters. This paper presents a general method for computing oscillator process and measurement noise parameters from an Allan variance characterization of the carrier phase offset measurements. Numerical results are presented using measured data from several N210 Universal Software Radio Peripherals (USRPs) at two different carrier frequencies. Using the estimated process and measurement noise parameters, the tracking performance is also evaluated on measured data from the USRPs and compared to theoretical predictions. Distributed beamforming and nullforming performance is also characterized using empirical phase prediction error statistics from the measured data.